Polytope of Type {34,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,6,4}*1632a
Also Known As : {{34,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1632,1097)
Rank : 4
Schlafli Type : {34,6,4}
Number of vertices, edges, etc : 34, 102, 12, 4
Order of s0s1s2s3 : 204
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {34,6,2}*816
3-fold quotients : {34,2,4}*544
6-fold quotients : {17,2,4}*272, {34,2,2}*272
12-fold quotients : {17,2,2}*136
17-fold quotients : {2,6,4}*96a
34-fold quotients : {2,6,2}*48
51-fold quotients : {2,2,4}*32
68-fold quotients : {2,3,2}*24
102-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)( 9, 10)
( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)( 26, 27)
( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)( 43, 44)
( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 60, 61)
( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 77, 78)
( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)
(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)
(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)
(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146)
(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)
(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)(179,180)
(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197);;
s1 := ( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)
( 18, 36)( 19, 35)( 20, 51)( 21, 50)( 22, 49)( 23, 48)( 24, 47)( 25, 46)
( 26, 45)( 27, 44)( 28, 43)( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)
( 34, 37)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)
( 60, 62)( 69, 87)( 70, 86)( 71,102)( 72,101)( 73,100)( 74, 99)( 75, 98)
( 76, 97)( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 90)
( 84, 89)( 85, 88)(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)
(110,114)(111,113)(120,138)(121,137)(122,153)(123,152)(124,151)(125,150)
(126,149)(127,148)(128,147)(129,146)(130,145)(131,144)(132,143)(133,142)
(134,141)(135,140)(136,139)(154,155)(156,170)(157,169)(158,168)(159,167)
(160,166)(161,165)(162,164)(171,189)(172,188)(173,204)(174,203)(175,202)
(176,201)(177,200)(178,199)(179,198)(180,197)(181,196)(182,195)(183,194)
(184,193)(185,192)(186,191)(187,190);;
s2 := ( 1, 18)( 2, 19)( 3, 20)( 4, 21)( 5, 22)( 6, 23)( 7, 24)( 8, 25)
( 9, 26)( 10, 27)( 11, 28)( 12, 29)( 13, 30)( 14, 31)( 15, 32)( 16, 33)
( 17, 34)( 52, 69)( 53, 70)( 54, 71)( 55, 72)( 56, 73)( 57, 74)( 58, 75)
( 59, 76)( 60, 77)( 61, 78)( 62, 79)( 63, 80)( 64, 81)( 65, 82)( 66, 83)
( 67, 84)( 68, 85)(103,171)(104,172)(105,173)(106,174)(107,175)(108,176)
(109,177)(110,178)(111,179)(112,180)(113,181)(114,182)(115,183)(116,184)
(117,185)(118,186)(119,187)(120,154)(121,155)(122,156)(123,157)(124,158)
(125,159)(126,160)(127,161)(128,162)(129,163)(130,164)(131,165)(132,166)
(133,167)(134,168)(135,169)(136,170)(137,188)(138,189)(139,190)(140,191)
(141,192)(142,193)(143,194)(144,195)(145,196)(146,197)(147,198)(148,199)
(149,200)(150,201)(151,202)(152,203)(153,204);;
s3 := ( 1,103)( 2,104)( 3,105)( 4,106)( 5,107)( 6,108)( 7,109)( 8,110)
( 9,111)( 10,112)( 11,113)( 12,114)( 13,115)( 14,116)( 15,117)( 16,118)
( 17,119)( 18,120)( 19,121)( 20,122)( 21,123)( 22,124)( 23,125)( 24,126)
( 25,127)( 26,128)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)
( 33,135)( 34,136)( 35,137)( 36,138)( 37,139)( 38,140)( 39,141)( 40,142)
( 41,143)( 42,144)( 43,145)( 44,146)( 45,147)( 46,148)( 47,149)( 48,150)
( 49,151)( 50,152)( 51,153)( 52,154)( 53,155)( 54,156)( 55,157)( 56,158)
( 57,159)( 58,160)( 59,161)( 60,162)( 61,163)( 62,164)( 63,165)( 64,166)
( 65,167)( 66,168)( 67,169)( 68,170)( 69,171)( 70,172)( 71,173)( 72,174)
( 73,175)( 74,176)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)
( 81,183)( 82,184)( 83,185)( 84,186)( 85,187)( 86,188)( 87,189)( 88,190)
( 89,191)( 90,192)( 91,193)( 92,194)( 93,195)( 94,196)( 95,197)( 96,198)
( 97,199)( 98,200)( 99,201)(100,202)(101,203)(102,204);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(204)!( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)
( 9, 10)( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)
( 26, 27)( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)
( 43, 44)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)
( 77, 78)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)
( 94, 95)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)
(111,112)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)
(128,129)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)
(145,146)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)
(179,180)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)
(196,197);
s1 := Sym(204)!( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)
( 9, 11)( 18, 36)( 19, 35)( 20, 51)( 21, 50)( 22, 49)( 23, 48)( 24, 47)
( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)( 30, 41)( 31, 40)( 32, 39)
( 33, 38)( 34, 37)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)
( 59, 63)( 60, 62)( 69, 87)( 70, 86)( 71,102)( 72,101)( 73,100)( 74, 99)
( 75, 98)( 76, 97)( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)
( 83, 90)( 84, 89)( 85, 88)(103,104)(105,119)(106,118)(107,117)(108,116)
(109,115)(110,114)(111,113)(120,138)(121,137)(122,153)(123,152)(124,151)
(125,150)(126,149)(127,148)(128,147)(129,146)(130,145)(131,144)(132,143)
(133,142)(134,141)(135,140)(136,139)(154,155)(156,170)(157,169)(158,168)
(159,167)(160,166)(161,165)(162,164)(171,189)(172,188)(173,204)(174,203)
(175,202)(176,201)(177,200)(178,199)(179,198)(180,197)(181,196)(182,195)
(183,194)(184,193)(185,192)(186,191)(187,190);
s2 := Sym(204)!( 1, 18)( 2, 19)( 3, 20)( 4, 21)( 5, 22)( 6, 23)( 7, 24)
( 8, 25)( 9, 26)( 10, 27)( 11, 28)( 12, 29)( 13, 30)( 14, 31)( 15, 32)
( 16, 33)( 17, 34)( 52, 69)( 53, 70)( 54, 71)( 55, 72)( 56, 73)( 57, 74)
( 58, 75)( 59, 76)( 60, 77)( 61, 78)( 62, 79)( 63, 80)( 64, 81)( 65, 82)
( 66, 83)( 67, 84)( 68, 85)(103,171)(104,172)(105,173)(106,174)(107,175)
(108,176)(109,177)(110,178)(111,179)(112,180)(113,181)(114,182)(115,183)
(116,184)(117,185)(118,186)(119,187)(120,154)(121,155)(122,156)(123,157)
(124,158)(125,159)(126,160)(127,161)(128,162)(129,163)(130,164)(131,165)
(132,166)(133,167)(134,168)(135,169)(136,170)(137,188)(138,189)(139,190)
(140,191)(141,192)(142,193)(143,194)(144,195)(145,196)(146,197)(147,198)
(148,199)(149,200)(150,201)(151,202)(152,203)(153,204);
s3 := Sym(204)!( 1,103)( 2,104)( 3,105)( 4,106)( 5,107)( 6,108)( 7,109)
( 8,110)( 9,111)( 10,112)( 11,113)( 12,114)( 13,115)( 14,116)( 15,117)
( 16,118)( 17,119)( 18,120)( 19,121)( 20,122)( 21,123)( 22,124)( 23,125)
( 24,126)( 25,127)( 26,128)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)
( 32,134)( 33,135)( 34,136)( 35,137)( 36,138)( 37,139)( 38,140)( 39,141)
( 40,142)( 41,143)( 42,144)( 43,145)( 44,146)( 45,147)( 46,148)( 47,149)
( 48,150)( 49,151)( 50,152)( 51,153)( 52,154)( 53,155)( 54,156)( 55,157)
( 56,158)( 57,159)( 58,160)( 59,161)( 60,162)( 61,163)( 62,164)( 63,165)
( 64,166)( 65,167)( 66,168)( 67,169)( 68,170)( 69,171)( 70,172)( 71,173)
( 72,174)( 73,175)( 74,176)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)
( 80,182)( 81,183)( 82,184)( 83,185)( 84,186)( 85,187)( 86,188)( 87,189)
( 88,190)( 89,191)( 90,192)( 91,193)( 92,194)( 93,195)( 94,196)( 95,197)
( 96,198)( 97,199)( 98,200)( 99,201)(100,202)(101,203)(102,204);
poly := sub<Sym(204)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope